How does a character gain the ability to make a full attack after a charge? Is there a feat or a spell? If not in core PF, where else did it exist?
The spell Beast Shape II, or the Druid's wildshape ability mimicking the same. I'm not aware of a PFRPG feat that allows pounce, but you might find something on the Archives of Nethys.
Zo
A barbarian with the beast totem rage power chain gains pounce at lvl 10, it is in the APG.
A mobile fighter archetype from the APG gives something like pounce -- but it isn't the same.
Isn't there also an archetype of the monk that pounce also?